Finite Group Databasebeta

← C31×#10994 #21467753

Subgroups — C31×#10994 #21467753

Order 7936.

1494 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#525C211yesmaximal, characteristic
2C2×C31×#421C211yesmaximal, characteristic, complemented
3C31×#2896C211yesmaximal, characteristic, complemented
4C2×C31×#407C211yesmaximal, characteristic, complemented
5C31×#2280C211yesmaximal, characteristic, complemented
6C31×#1733C211yesmaximal, characteristic, complemented
7C2×C31×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
8C22×#41×C31C2211yescharacteristic
9C24×C4×C31C2211yescharacteristic
10C22×M16×C31C2211yescharacteristic
11C22×M16×C31C2211yescharacteristic
12C31×#525—22no—
13C31×#525—22no—
14C31×#525—22no—
15C31×#525C414yescomplemented
16C2×C31×#123—21no—
17C2×C31×C22⋊Q8—21no—
18C2×C31×#121—21no—
19C2×C31×#120—21no—
20C2×C4×D4×C31—22no—
21C2×C31×#117C2211yescharacteristic
22C2×C31×#117C2211yescharacteristic
23C2×C31×#117C2211yescharacteristic
24C31×#421—22no—
25C31×#421—22no—
26C2×C31×#104—22no—
27C31×#419—21no—
28C31×#418—21no—
29C31×#417—22no—
30C31×#416—22no—
31C31×#407—22no—
32C31×#407—22no—
33C2×C31×C22⋊C8—22no—
34C31×#381—21no—
35C31×#380—22no—
36C31×#379—21no—
37C4×C22⋊C4×C31—22no—
38C31×#339—22no—
39C31×H(3,ℤ/4)—22no—
40C25×C31D411yescharacteristic
41C2×#41×C31—21no—
42C2×#41×C31—21no—
43C2×#41×C31—21no—
44C2×#41×C31—21no—
45C2×#41×C31—21no—
46C2×#41×C31—21no—
47C2×#41×C31—21no—
48C2×#41×C31—21no—
49C2×#41×C31—21no—
50C2×#41×C31—21no—
51C2×#41×C31C2×C412yes—
52C2×#41×C31D412yes—
53C22×Q8×C31D411yescharacteristic
54C22×D4×C31—22no—
55C22×D4×C31—21no—
56C22×D4×C31D411yescharacteristic
57C23×C4×C31—21no—
58C23×C4×C31—21no—
59C23×C4×C31—21no—
60C23×C4×C31—21no—
61C23×C4×C31—21no—
62C23×C4×C31—21no—
63C23×C4×C31—21no—
64C23×C4×C31—21no—
65C23×C4×C31—21no—
66C23×C4×C31—21no—
67C23×C4×C31—21no—
68C23×C4×C31—21no—
69C23×C4×C31—21no—
70C23×C4×C31C2×C412yes—
71C23×C4×C31D411yescharacteristic
72C23×C4×C31D412yes—
73C23×C4×C31C2311yescharacteristic
74C2×M16×C31—21no—
75C2×M16×C31—21no—
76C2×M16×C31—21no—
77C2×M16×C31—21no—
78C2×M16×C31—21no—
79C2×M16×C31—21no—
80C2×M16×C31—21no—
81C2×M16×C31—21no—
82C2×M16×C31—21no—
83C2×M16×C31—21no—
84C2×M16×C31—21no—
85C2×M16×C31D412yescomplemented
86C22×C8×C31—21no—
87C22×C8×C31D412yescomplemented
88C31×#123—24no—
89C31×#123—24no—
90C31×C22⋊Q8—24no—
91C31×C22⋊Q8—24no—
92C31×#121—24no—
93C31×#121—24no—
94C31×#120—24no—
95C31×#120—24no—
96C4×D4×C31—28no—
97C4×D4×C31—28no—
98C31×#117—21no—
99C31×#117—21no—
100C31×#117—21no—
101C31×#117—21no—
102C31×#117—21no—
103C31×#117—21no—
104C31×#117—21no—
105C31×#117—21no—
106C31×#117—21no—
107C31×#117—21no—
108C31×#117C2×C412yes—
109C31×#117D412yes—
110C2×C4⋊C4×C31—22no—
111C2×C4⋊C4×C31—21no—
112C2×C4⋊C4×C31—21no—
113C2×C4⋊C4×C31D412yescomplemented
114C2×C22⋊C4×C31—22no—
115C2×C22⋊C4×C31—22no—
116C2×C22⋊C4×C31—21no—
117C2×C22⋊C4×C31—24no—
118C2×C22⋊C4×C31—21no—
119C2×C22⋊C4×C31—21no—
120C2×C42×C31—21no—
121C2×C42×C31D412yes—
122C2×C42×C31D412yescomplemented
123C31×#104—28no—
124C31×#103—24no—
125C31×#102—24no—
126C31×C22⋊C8—28no—
127C31×#95—24no—
128C24×C31—21no—
129C24×C31—21no—
130C24×C31—21no—
131C24×C31—21no—
132C24×C31—21no—
133C24×C31—21no—
134C24×C31—21no—
135C24×C31—44no—
136C24×C31C22⋊C412yes—
137C24×C31C2×D411yescharacteristic
138#41×C31—22no—
139#41×C31—22no—
140#41×C31—22no—
141#41×C31—22no—
142#41×C31—22no—
143#41×C31—22no—
144#41×C31—22no—
145#41×C31—22no—
146#41×C31—41no—
147#41×C31—41no—
148#41×C31—41no—
149#41×C31—41no—
150#41×C31—41no—
151#41×C31—41no—
152#41×C31—41no—
153#41×C31—41no—
154C2×Q8×C31—21no—
155C2×Q8×C31—21no—
156C2×Q8×C31—21no—
157C2×Q8×C31—21no—
158C2×Q8×C31—21no—
159C2×Q8×C31C22⋊C412yescomplemented
160C2×D4×C31—28no—
161C2×D4×C31—22no—
162C2×D4×C31—22no—
163C2×D4×C31—21no—
164C2×D4×C31—21no—
165C2×D4×C31—21no—
166C2×D4×C31—21no—
167C2×D4×C31—21no—
168C2×D4×C31—48no—
169C2×D4×C31—41no—
170C2×D4×C31—41no—
171C2×D4×C31—41no—
172C2×D4×C31—41no—
173C2×D4×C31C22⋊C412yescomplemented
174C22×C4×C31—21no—
175C22×C4×C31—22no—
176C22×C4×C31—21no—
177C22×C4×C31—21no—
178C22×C4×C31—21no—
179C22×C4×C31—21no—
180C22×C4×C31—21no—
181C22×C4×C31—21no—
182C22×C4×C31—22no—
183C22×C4×C31—22no—
184C22×C4×C31—22no—
185C22×C4×C31—22no—
186C22×C4×C31—22no—
187C22×C4×C31—22no—
188C22×C4×C31—22no—
189C22×C4×C31—22no—
190C22×C4×C31—22no—
191C22×C4×C31—22no—
192C22×C4×C31—22no—
193C22×C4×C31—22no—
194C22×C4×C31—22no—
195C22×C4×C31—22no—
196C22×C4×C31—22no—
197C22×C4×C31—22no—
198C22×C4×C31—41no—
199C22×C4×C31—41no—
200C22×C4×C31—41no—
201C22×C4×C31—41no—
202C22×C4×C31—41no—
203C22×C4×C31—41no—
204C22×C4×C31—41no—
205C22×C4×C31—41no—
206C22×C4×C31—41no—
207C22×C4×C31—41no—
208C22×C4×C31—41no—
209C22×C4×C31—41no—
210C22×C4×C31—41no—
211C22×C4×C31—41no—
212C22×C4×C31—41no—
213C22×C4×C31—41no—
214C22×C4×C31—41no—
215C22×C4×C31—41no—
216C22×C4×C31—41no—
217C22×C4×C31—41no—
218C22×C4×C31C22⋊C412yes—
219C22×C4×C31C22×C411yescharacteristic
220C22×C4×C31C2×D411yescharacteristic
221C22×C4×C31C2×D411yescharacteristic
222C22×C4×C31C2×D411yescharacteristic
223C22×C4×C31C2×D411yescharacteristic
224C22×C4×C31C2×D411yescharacteristic
225C22×C4×C31C2×D411yescharacteristic
226C22×C4×C31C2×D411yescharacteristic
227C22×C4×C31C2×D411yescharacteristic
228C22×C4×C31C2×D411yescharacteristic
229C22×C4×C31#4111yescharacteristic
230C22×C4×C31#4111yescharacteristic
231C22×C4×C31#4111yescharacteristic
232C22×C4×C31#4111yescharacteristic
233M16×C31—22no—
234M16×C31—22no—
235M16×C31—41no—
236M16×C31—41no—
237M16×C31—41no—
238M16×C31—41no—
239M16×C31—41no—
240M16×C31—41no—
241C2×C8×C31—22no—
242C2×C8×C31—22no—
243C2×C8×C31—22no—
244C2×C8×C31—22no—
245C2×C8×C31—41no—
246C2×C8×C31—41no—
247C4⋊C4×C31—28no—
248C4⋊C4×C31—22no—
249C4⋊C4×C31—22no—
250C4⋊C4×C31—22no—
251C4⋊C4×C31—22no—
252C4⋊C4×C31—41no—
253C4⋊C4×C31—41no—
254C22⋊C4×C31—28no—
255C22⋊C4×C31—28no—
256C22⋊C4×C31—22no—
257C22⋊C4×C31—22no—
258C22⋊C4×C31—48no—
259C22⋊C4×C31—41no—
260C22⋊C4×C31—41no—
261C22⋊C4×C31—41no—
262C22⋊C4×C31—41no—
263C42×C31—22no—
264C42×C31—22no—
265C42×C31—22no—
266C42×C31—41no—
267C42×C31—41no—
268C42×C31C22⋊C414yescomplemented
269#10994C3111yesmaximal, characteristic, direct product factor, Sylow
270C23×C31—24no—
271C23×C31—24no—
272C23×C31—24no—
273C23×C31—22no—
274C23×C31—22no—
275C23×C31—22no—
276C23×C31—22no—
277C23×C31—44no—
278C23×C31—42no—
279C23×C31—42no—
280C23×C31—42no—
281C23×C31—42no—
282C23×C31—44no—
283C23×C31—44no—
284C23×C31—44no—
285C23×C31—44no—
286C23×C31—41no—
287C23×C31—41no—
288C23×C31—41no—
289C23×C31—41no—
290C23×C31—41no—
291C23×C31—41no—
292C23×C31C2×C22⋊C411yescharacteristic
293C23×C31#12011yescharacteristic
294C23×C31#12011yescharacteristic
295C23×C31#12011yescharacteristic
296C23×C31#12111yescharacteristic
297C23×C31#12111yescharacteristic
298C23×C31#12311yescharacteristic
299Q8×C31—22no—
300Q8×C31—22no—
301Q8×C31—41no—
302Q8×C31—41no—
303D4×C31—22no—
304D4×C31—22no—
305D4×C31—416no—
306D4×C31—42no—
307D4×C31—42no—
308D4×C31—42no—
309D4×C31—42no—
310D4×C31—41no—
311D4×C31—41no—
312C2×C4×C31—24no—
313C2×C4×C31—22no—
314C2×C4×C31—22no—
315C2×C4×C31—22no—
316C2×C4×C31—22no—
317C2×C4×C31—44no—
318C2×C4×C31—41no—
319C2×C4×C31—41no—
320C2×C4×C31—41no—
321C2×C4×C31—41no—
322C2×C4×C31—41no—
323C2×C4×C31—41no—
324C2×C4×C31—42no—
325C2×C4×C31—42no—
326C2×C4×C31—42no—
327C2×C4×C31—42no—
328C2×C4×C31—42no—
329C2×C4×C31—42no—
330C2×C4×C31—42no—
331C2×C4×C31—42no—
332C2×C4×C31—42no—
333C2×C4×C31—42no—
334C2×C4×C31—42no—
335C2×C4×C31—42no—
336C2×C4×C31—44no—
337C2×C4×C31—44no—
338C2×C4×C31—42no—
339C2×C4×C31—42no—
340C2×C4×C31C2×C22⋊C411yescharacteristic
341C2×C4×C31C2×C22⋊C411yescharacteristic
342C2×C4×C31C4×D411yescharacteristic
343C2×C4×C31C4×D411yescharacteristic
344C2×C4×C31C4×D411yescharacteristic
345C2×C4×C31C4×D411yescharacteristic
346C2×C4×C31#12011yescharacteristic
347C2×C4×C31#12011yescharacteristic
348C2×C4×C31#12011yescharacteristic
349C2×C4×C31#12011yescharacteristic
350C2×C4×C31#12011yescharacteristic
351C2×C4×C31#12111yescharacteristic
352C2×C4×C31#12111yescharacteristic
353C2×C4×C31#12111yescharacteristic
354C2×C4×C31#12111yescharacteristic
355C2×C4×C31#12111yescharacteristic
356C2×C4×C31#12111yescharacteristic
357C2×C4×C31#12111yescharacteristic
358C2×C4×C31#12111yescharacteristic
359C2×C4×C31#12111yescharacteristic
360C2×C4×C31#12111yescharacteristic
361C2×C4×C31#12311yescharacteristic
362C2×C4×C31#12311yescharacteristic
363C2×C4×C31#12311yescharacteristic
364C2×C4×C31#12411yescharacteristic
365C2×C4×C31#12411yescharacteristic
366C2×C4×C31#12711yescharacteristic
367C2×C4×C31#12711yescharacteristic
368C8×C31—42no—
369C8×C31—42no—
370C2×#525C2×C3111yescharacteristic
371C2×#421C2×C3111yescharacteristic, complemented
372#2896C2×C3111yescharacteristic, complemented
373C2×#407C2×C3111yescharacteristic, complemented
374#2280C2×C3111yescharacteristic, complemented
375#1733C2×C3111yescharacteristic, complemented
376C2×H(3,ℤ/4)C2×C3111yescharacteristic, complemented
377C22×C31—22no—
378C22×C31—22no—
379C22×C31—22no—
380C22×C31—24no—
381C22×C31—24no—
382C22×C31—24no—
383C22×C31—41no—
384C22×C31—41no—
385C22×C31—41no—
386C22×C31—41no—
387C22×C31—42no—
388C22×C31—44no—
389C22×C31—42no—
390C22×C31—42no—
391C22×C31—44no—
392C22×C31—44no—
393C22×C31—44no—
394C22×C31—42no—
395C22×C31—44no—
396C22×C31—42no—
397C22×C31—82no—
398C22×C31—82no—
399C22×C31#37911yescharacteristic
400C22×C31#38611yescharacteristic
401C22×C31#38611yescharacteristic
402C22×C31#39211yescharacteristic
403C22×C31#39211yescharacteristic
404C22×C31#39411yescharacteristic
405C22×C31#39411yescharacteristic
406C4×C31—44no—
407C4×C31—42no—
408C4×C31—42no—
409C4×C31—82no—
410C4×C31—82no—
411C4×C31#38611yescharacteristic
412C4×C31#38611yescharacteristic
413C4×C31#39011yescharacteristic
414C4×C31#39011yescharacteristic
415C4×C31#39211yescharacteristic
416C4×C31#39211yescharacteristic
417C4×C31#39411yescharacteristic
418C4×C31#39411yescharacteristic
419C22×#41C22×C3111yescharacteristic
420C24×C4C22×C3111yescharacteristic
421C22×M16C22×C3111yescharacteristic
422C22×M16C22×C3111yescharacteristic
423#525—22no—
424#525—22no—
425#525—22no—
426#525C4×C3114yescomplemented
427C2×#123—21no—
428C2×C22⋊Q8—21no—
429C2×#121—21no—
430C2×#120—21no—
431C2×C4×D4—22no—
432C2×#117C22×C3111yescharacteristic
433C2×#117C22×C3111yescharacteristic
434C2×#117C22×C3111yescharacteristic
435#421—22no—
436#421—22no—
437C2×#104—22no—
438#419—21no—
439#418—21no—
440#417—22no—
441#416—22no—
442#407—22no—
443#407—22no—
444C2×C22⋊C8—22no—
445#381—21no—
446#380—22no—
447#379—21no—
448C4×C22⋊C4—22no—
449#339—22no—
450H(3,ℤ/4)—22no—
451C2×C31—21no—
452C2×C31—21no—
453C2×C31—21no—
454C2×C31—21no—
455C2×C31—21no—
456C2×C31—21no—
457C2×C31—44no—
458C2×C31—82no—
459C2×C31#143811yescharacteristic
460C2×C31#201012yes—
461C25D4×C3111yescharacteristic
462C2×#41—21no—
463C2×#41—21no—
464C2×#41—21no—
465C2×#41—21no—
466C2×#41—21no—
467C2×#41—21no—
468C2×#41—21no—
469C2×#41—21no—
470C2×#41—21no—
471C2×#41—21no—
472C2×#41C2×C4×C3112yes—
473C2×#41D4×C3112yes—
474C22×Q8D4×C3111yescharacteristic
475C22×D4—22no—
476C22×D4—21no—
477C22×D4D4×C3111yescharacteristic
478C23×C4—21no—
479C23×C4—21no—
480C23×C4—21no—
481C23×C4—21no—
482C23×C4—21no—
483C23×C4—21no—
484C23×C4—21no—
485C23×C4—21no—
486C23×C4—21no—
487C23×C4—21no—
488C23×C4—21no—
489C23×C4—21no—
490C23×C4—21no—
491C23×C4C2×C4×C3112yes—
492C23×C4D4×C3111yescharacteristic
493C23×C4D4×C3112yes—
494C23×C4C23×C3111yescharacteristic
495C2×M16—21no—
496C2×M16—21no—
497C2×M16—21no—
498C2×M16—21no—
499C2×M16—21no—
500C2×M16—21no—
501C2×M16—21no—
502C2×M16—21no—
503C2×M16—21no—
504C2×M16—21no—
505C2×M16—21no—
506C2×M16D4×C3112yescomplemented
507C22×C8—21no—
508C22×C8D4×C3112yescomplemented
509#123—24no—
510#123—24no—
511C22⋊Q8—24no—
512C22⋊Q8—24no—
513#121—24no—
514#121—24no—
515#120—24no—
516#120—24no—
517C4×D4—28no—
518C4×D4—28no—
519#117—21no—
520#117—21no—
521#117—21no—
522#117—21no—
523#117—21no—
524#117—21no—
525#117—21no—
526#117—21no—
527#117—21no—
528#117—21no—
529#117C2×C4×C3112yes—
530#117D4×C3112yes—
531C2×C4⋊C4—22no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4D4×C3112yescomplemented
535C2×C22⋊C4—22no—
536C2×C22⋊C4—22no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—24no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C42—21no—
542C2×C42D4×C3112yes—
543C2×C42D4×C3112yescomplemented
544#104—28no—
545#103—24no—
546#102—24no—
547C22⋊C8—28no—
548#95—24no—
549C31#1099411yescharacteristic, direct product factor, Sylow
550C24—21no—
551C24—21no—
552C24—21no—
553C24—21no—
554C24—21no—
555C24—21no—
556C24—21no—
557C24—44no—
558C24C22⋊C4×C3112yes—
559C24C2×D4×C3111yescharacteristic
560#41—22no—
561#41—22no—
562#41—22no—
563#41—22no—
564#41—22no—
565#41—22no—
566#41—22no—
567#41—22no—
568#41—41no—
569#41—41no—
570#41—41no—
571#41—41no—
572#41—41no—
573#41—41no—
574#41—41no—
575#41—41no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8C22⋊C4×C3112yescomplemented
582C2×D4—28no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—48no—
591C2×D4—41no—
592C2×D4—41no—
593C2×D4—41no—
594C2×D4—41no—
595C2×D4C22⋊C4×C3112yescomplemented
596C22×C4—21no—
597C22×C4—22no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—41no—
621C22×C4—41no—
622C22×C4—41no—
623C22×C4—41no—
624C22×C4—41no—
625C22×C4—41no—
626C22×C4—41no—
627C22×C4—41no—
628C22×C4—41no—
629C22×C4—41no—
630C22×C4—41no—
631C22×C4—41no—
632C22×C4—41no—
633C22×C4—41no—
634C22×C4—41no—
635C22×C4—41no—
636C22×C4—41no—
637C22×C4—41no—
638C22×C4—41no—
639C22×C4—41no—
640C22×C4C22⋊C4×C3112yes—
641C22×C4C22×C4×C3111yescharacteristic
642C22×C4C2×D4×C3111yescharacteristic
643C22×C4C2×D4×C3111yescharacteristic
644C22×C4C2×D4×C3111yescharacteristic
645C22×C4C2×D4×C3111yescharacteristic
646C22×C4C2×D4×C3111yescharacteristic
647C22×C4C2×D4×C3111yescharacteristic
648C22×C4C2×D4×C3111yescharacteristic
649C22×C4C2×D4×C3111yescharacteristic
650C22×C4C2×D4×C3111yescharacteristic
651C22×C4#41×C3111yescharacteristic
652C22×C4#41×C3111yescharacteristic
653C22×C4#41×C3111yescharacteristic
654C22×C4#41×C3111yescharacteristic
655M16—22no—
656M16—22no—
657M16—41no—
658M16—41no—
659M16—41no—
660M16—41no—
661M16—41no—
662M16—41no—
663C2×C8—22no—
664C2×C8—22no—
665C2×C8—22no—
666C2×C8—22no—
667C2×C8—41no—
668C2×C8—41no—
669C4⋊C4—28no—
670C4⋊C4—22no—
671C4⋊C4—22no—
672C4⋊C4—22no—
673C4⋊C4—22no—
674C4⋊C4—41no—
675C4⋊C4—41no—
676C22⋊C4—28no—
677C22⋊C4—28no—
678C22⋊C4—22no—
679C22⋊C4—22no—
680C22⋊C4—48no—
681C22⋊C4—41no—
682C22⋊C4—41no—
683C22⋊C4—41no—
684C22⋊C4—41no—
685C42—22no—
686C42—22no—
687C42—22no—
688C42—41no—
689C42—41no—
690C42C22⋊C4×C3114yescomplemented
691C23—24no—
692C23—24no—
693C23—24no—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—22no—
698C23—44no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—44no—
704C23—44no—
705C23—44no—
706C23—44no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23C2×C22⋊C4×C3111yescharacteristic
714C23C31×#12011yescharacteristic
715C23C31×#12011yescharacteristic
716C23C31×#12011yescharacteristic
717C23C31×#12111yescharacteristic
718C23C31×#12111yescharacteristic
719C23C31×#12311yescharacteristic
720Q8—22no—
721Q8—22no—
722Q8—41no—
723Q8—41no—
724D4—22no—
725D4—22no—
726D4—416no—
727D4—42no—
728D4—42no—
729D4—42no—
730D4—42no—
731D4—41no—
732D4—41no—
733C2×C4—24no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—44no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4C2×C22⋊C4×C3111yescharacteristic
762C2×C4C2×C22⋊C4×C3111yescharacteristic
763C2×C4C4×D4×C3111yescharacteristic
764C2×C4C4×D4×C3111yescharacteristic
765C2×C4C4×D4×C3111yescharacteristic
766C2×C4C4×D4×C3111yescharacteristic
767C2×C4C31×#12011yescharacteristic
768C2×C4C31×#12011yescharacteristic
769C2×C4C31×#12011yescharacteristic
770C2×C4C31×#12011yescharacteristic
771C2×C4C31×#12011yescharacteristic
772C2×C4C31×#12111yescharacteristic
773C2×C4C31×#12111yescharacteristic
774C2×C4C31×#12111yescharacteristic
775C2×C4C31×#12111yescharacteristic
776C2×C4C31×#12111yescharacteristic
777C2×C4C31×#12111yescharacteristic
778C2×C4C31×#12111yescharacteristic
779C2×C4C31×#12111yescharacteristic
780C2×C4C31×#12111yescharacteristic
781C2×C4C31×#12111yescharacteristic
782C2×C4C31×#12311yescharacteristic
783C2×C4C31×#12311yescharacteristic
784C2×C4C31×#12311yescharacteristic
785C2×C4C31×#12411yescharacteristic
786C2×C4C31×#12411yescharacteristic
787C2×C4C31×#12711yescharacteristic
788C2×C4C31×#12711yescharacteristic
789C8—42no—
790C8—42no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—24no—
795C22—24no—
796C22—24no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—42no—
802C22—44no—
803C22—42no—
804C22—42no—
805C22—44no—
806C22—44no—
807C22—44no—
808C22—42no—
809C22—44no—
810C22—42no—
811C22—82no—
812C22—82no—
813C22C31×#37911yescharacteristic
814C22C31×#38611yescharacteristic
815C22C31×#38611yescharacteristic
816C22C31×#39211yescharacteristic
817C22C31×#39211yescharacteristic
818C22C31×#39411yescharacteristic
819C22C31×#39411yescharacteristic
820C4—44no—
821C4—42no—
822C4—42no—
823C4—82no—
824C4—82no—
825C4C31×#38611yescharacteristic
826C4C31×#38611yescharacteristic
827C4C31×#39011yescharacteristic
828C4C31×#39011yescharacteristic
829C4C31×#39211yescharacteristic
830C4C31×#39211yescharacteristic
831C4C31×#39411yescharacteristic
832C4C31×#39411yescharacteristic
833C2—21no—
834C2—21no—
835C2—21no—
836C2—21no—
837C2—21no—
838C2—21no—
839C2—44no—
840C2—82no—
841C2C31×#143811yescharacteristic
842C2C31×#201012yes—
subgroupG/H
centerC2×C4×C31#127
commutatorC22×C4C22×C4×C31
Frattini, cosocleC23×C4C23×C31
socleC22×C31#392
prime radicalC2×C31×#525C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C31 ◁ C23×C4×C31 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×C31×#421C2semidirect
3. C31×#2896C2semidirect
4. C2×C31×#407C2semidirect
5. C31×#2280C2semidirect
6. C31×#1733C2semidirect
7. C2×C31×H(3,ℤ/4)C2semidirect
15. C31×#525C4semidirect
85. C2×M16×C31D4semidirect
87. C22×C8×C31D4semidirect
113. C2×C4⋊C4×C31D4semidirect
122. C2×C42×C31D4semidirect
159. C2×Q8×C31C22⋊C4semidirect
173. C2×D4×C31C22⋊C4semidirect
268. C42×C31C22⋊C4semidirect
269. #10994C31direct (N × H)
371. C2×#421C2×C31semidirect
372. #2896C2×C31semidirect
373. C2×#407C2×C31semidirect
374. #2280C2×C31semidirect
375. #1733C2×C31semidirect
376. C2×H(3,ℤ/4)C2×C31semidirect
426. #525C4×C31semidirect
506. C2×M16D4×C31semidirect
508. C22×C8D4×C31semidirect
534. C2×C4⋊C4D4×C31semidirect
543. C2×C42D4×C31semidirect
549. C31#10994direct (N × H)
581. C2×Q8C22⋊C4×C31semidirect
595. C2×D4C22⋊C4×C31semidirect
690. C42C22⋊C4×C31semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C31×#5252
C2×C31×#4212
C31×#28962
C2×C31×#4072
C31×#22802
C31×#17332
C2×C31×H(3,ℤ/4)2
#1099431